def test_fixedpoint():
"""
Test that the minimum of a quadratic is a fixed point
"""
def f_df(x):
return 0.5 * x.T.dot(x), x
xstar = np.array([0., 0.])
gen = sgd(f_df, xstar).__iter__()
assert np.allclose(next(gen), xstar)
def test_quadratic_bowl():
"""
Test optimization in a quadratic bowl
"""
t = np.linspace(0, 2*np.pi, 100)
tol = 1e-3
theta_true = [np.sin(t), np.cos(t)]
theta_init = [np.cos(t), np.sin(t)]
def f_df(theta):
obj = 0.5*(theta[0]-theta_true[0])**2 + 0.5*(theta[1]-theta_true[1])**2
grad = [theta[0]-theta_true[0], theta[1]-theta_true[1]]
return np.sum(obj), grad
opt = sgd(f_df, theta_init, learning_rate=1e-2)
opt.display = None
opt.run(maxiter=1e3)
for theta in zip(opt.theta, theta_true):
assert np.linalg.norm(theta[0] - theta[1]) <= tol